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Spectral properties of the massless relativistic harmonic oscillator

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
253
Issue
10
Identifiers
DOI: 10.1016/j.jde.2012.07.010
Keywords
  • Cauchy Process
  • Fractional Schrödinger Operator
  • Spectrum
  • Trace Asymptotics
  • Decay Of Eigenfunctions
  • Heat Kernel
  • Airy Function

Abstract

Abstract The spectral properties of the pseudo-differential operator(−d2/dx2)1/2+x2 are analyzed by a combination of functional integration methods and direct analysis. We obtain a representation of its eigenvalues and eigenfunctions, prove precise asymptotic formulae, and establish various analytic properties. We also derive trace asymptotics and heat kernel estimates.

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